1. Field of the Invention
Embodiments of the present invention are directed in general to high resolution and high-sensitivity detection and/or profiling of the electromagnetic impedance of a substance. More specifically, the present invention is directed to systems and methods that use an evanescent wave probe.
2. State of the Art
In the discussion of the state of the art that follows, reference is made to certain structures and/or methods. However, the following references should not be construed as an admission that these structures and/or methods constitute prior art. Applicants expressly reserve the right to demonstrate that such structures and/or methods do not qualify as prior art against the present invention.
Classical Limitations
From classical microscopy theory, the diffraction-limited resolution of a microscope is primary determined by the wavelength of the wave used to interact with the sample. For example, the smallest feature that an optical microscope can resolve is about:
  δ  =      0.61    ⁢          λ      NA      where NA=n sin θ is the numerical aperture, n the refractive index of media, θ the aperture angle of the objective, and λ the wavelength of the electromagnetic radiation interacting with the sample. Since the wavelength of GHz microwave is in centimeter range, the limited resolving ability of a classical diffraction-limited microscope prevents RF/microwave electromagnetic properties (which include electric impedance) of small sized samples such as arrayed samples on a high density materials chip from being characterized. These conclusions are based on classical propagating wave theory.Evanescent Waves
The term evanescent wave in the context of this disclosure refers to electromagnetic waves with wave-vectors having an imaginary component that does not originate from dissipation. In electromagnetic wave theory, evanescent waves are the photonic equivalent of electron waves in quantum mechanics existing within a classically forbidden region (in other words, within a barrier). In the far-field description of electromagnetic waves, an orthogonal eigenfunction set of Hilbert space is chosen as the plane waves whose wave vectors are any real number satisfying the Helmholtz equation, and as a consequence, they are propagating waves.
Any propagating wave (for example, a propagating spherical wave) can be expanded as the superposition of such plane waves. The magnitudes of the wave vectors are determined soley by the frequency and speed of light in accordance with the Helmholtz equation, i.e. k=2πf√{square root over (εμ)}=2π/λ=√{square root over (kx2+ky2+kz2)}. For propagating waves, kx, ky, and kz are real numbers and thus must be smaller than k (in free space, k=k0). These waves only have a resolving power on the order of λ. However, these plane waves cannot construct, for example, a spherical wave whose wave front has a radius less than the wavelength λ. Therefore, a true complete set of Hilbert space should include plane waves whose wave vectors are any complex number satisfying the Maxwell equation to construct such a spherical wave. Since imaginary wave vectors are allowed, the components (kx, ky, kz) can then be any value and still satisfy the Maxwell equation.
The “plane waves” here whose lateral components kr=√{square root over (kx2+ky2 )} are larger than k will have a higher lateral resolving power, the resolving power being on the order of 1/kr. However, since they must have imaginary components kz to satisfy the Helmholtz equation, they are “evanescent,” and cannot propagate much further than a distance corresponding to a wavelength λ. A metal sphere or tip fed by a wave source with a radius of R0 (<<λ) will generate evanescent waves that form a spherical wave on the metal surface satisfying the boundary conditions, where the sperical waves have wave vectors ranging up to kr˜1/R0, and resolving power up to ˜R0. Interaction between the tip and sample (where the sample may have a high effective dielectric constant) may further increase the resolving power. For example, if g is the distance between the tip and the sample, resolutions on the order of √{square root over (gR0 )} may be obtained for for conducting materials as a result of decreasing the effective tip radius from polarizing effect. Since these waves decay over a distance R0 in free space, the sample has to be brought to within R0 of the tip to realize a strong interaction. Note these waves are not necessarily evanescent in conducting materials since the wave vector kc=2πf√{square root over (εμ(1+iσ/ωε))} is many orders of magnitude larger than that in free space.
Evanescent Wave Probes
Evanescent wave probes (EWP) refer to probes that emit evanescent electromagnetic waves. An instrument configured to scan an EWP across the surface of a sample constitutes an evanescent-wave microscope, which may be classified as one type of a scanning probe microscope (SPM). The first scanning probe microscope was probably the evanescent photon microscope envisioned by E. H. Synge in 1928. Fraint and Soohoo independently demonstrated this idea at microwave frequencies in 1959 and 1962, respectively, although the work by Ash and Nicholls 10 years later is often credited in literature. In recent years many different types of SPMs have been proposed and developed, largely due to the impact of the invention of the scanning tunneling microscope (STM), which itself may be viewed as an evanescent de Broglie wave microscope.
Until recently, carrying out methods of microscopy to quantify various materials properties, such as complex dielectric constant and electrical conductivity, have been virtually impossible. The difficulty arises from two major barriers. First, in all SPMs the microscopy signal is a convolution of topography and physical properties. Separating them requires measuring at least two independent signals simultaneously. The development of the scanning near-field optical microscope (SNOM) provided this capability by implementing shear force detection in addition to optical signal detection. Second, a detailed field configuration in the tip-sample region has to be solved, which subsequently gives rise to solutions that relate the signals explicitly to tip-sample distance and physical properties. These relations can then also be used for tip-sample distance feedback control to obtain simultaneously quantitative topography and physical property images. Although numerical methods based on finite element analysis have been used to solve the field distribution around a SNOM tip, the approach is not practical in routine applications.
In order to make measurements of the electrical impedance of a material, which would be tremendously useful to a broad range of applications, the evanescent (or near-field) microwave microscopy was suggested. Previous efforts took advantage of aperture or tapered waveguide probe configurations but when operating below the cut-off frequency, these probes suffer severely from waveguide decay. For example, tapered waveguide probes were widely used in NSOM, though they suffered from a typical attenuation of 10−3 to 10−6. As realized by Soohoo in 1962, a linear improvement in resolution can result in an exponential reduction in sensitivity. As a result, it is very hard to reconcile the conflict between resolution and sensitivity. Chu realized the conflict, and suggested using a transmission line probe with a reduced cross-section and sharp tip in 1988. However, as the resolution is also determined by the cross-section of the transmission line probe, further improvement to sub-micron resolution (if practical) still causes significant transmission line decay. Meanwhile, the unshielded far-field components around the tip in the transmission line probe significantly limit the resolution and capability for carrying out quantitative analysis.
It is perhaps beneficial to provide a historic perspective that to the best of the inventors' knowledge, outlines the various techniques, and efforts that have been made in the field. Frait and Soohoo were the first to independently demonstrate, in 1959 and 1962, respectively, similar evanescent microwave microscopes using the microwave cavity with a small aperture. Soohoo used the instrument to study the local properties of magnetic materials based on the ferromagnetic resonant absorption of microwaves. He was also the first to realize the conflict between spatial resolution and sensitivity that is inherent when taking the aperture approach. Bryant and Gunn (1965) were probably the first to use a tapered coaxial transmission line probe to study the local conductivity of materials, achieving a resolution of 1 mm. Ash and Nicholls published a paper in 1972 emphasizing the aperture approach. They are probably the first to demonstrate the super-resolution on dielectrics (although they were often mistakenly credited in the literature as having been the first to demonstrate the feasibility of an evanescent microwave microscope). In 1984, Massey discussed microscopy with scanned evanescent waves from an aperture, and tested the theory at 450 MHz.
A variety of studies have been published in the literature that investigated the resolution that is possible in metals. These reports are misleading, however, since the wavelength of microwaves in metals is at least four orders of magnitude smaller than in air, and smaller than the resolution those studies demonstrated.
It is doubtful these early pioneers were aware of the theoretic proposal made by Synge in 1928, and were probably not even aware of each other's work.
In 1988, Fee, Chu and Hansch published a paper that explicitly pointed out the limitation of the aperture type probe in near-field microscopy, and suggested using a coaxial transmission line with a very small cross section to obtain high resolution with significantly less loss. They also tested such a probe on metal, and pointed out that protruding and sharpening the center conductor of the probe could improve resolution. Wang et al in 1987 and 1990 demonstrated an evanescent microwave microscope based on a scanned tapered open (electric dipole) and closed (magnetic dipole) end of a microstrip resonator. Tabib-Azar et al. in 1993 discussed a similar approach. Several other groups have been actively implementing transmission line type probes in evanescent microwave microscopy studies, including van der Weide et al. and Anlage et al.
Recently, there has been renewed interest in designing new cavity and/or waveguide based structures. Golosovsky and Davidov, in 1996, demonstrated an open narrow slid structure in a waveguide, similar to what Gutmann et al. demostrated in 1987. These designs exhibit a much improved energy transmission relative to the aperture structure. Bae et al. discussed a similar approach in 1997. Grober et al proposed yet another bow-tie antenna structure as the scanning probe.
Thus it may be seen that much effort has been devoted to improving resolution and sensitivity in evanescent wave microwave microscopes, with specific attention having been given to probe design. Although advances have been made, there is still a need in the art for improvement such that resolution may be enhanced simultaneously with sensitivity.